Study null sectional curvatures in warped product spaces.
problem Investigate null sectional curvatures in warped product spaces.
method Derive formulas for null sectional curvatures of specific warped product models.
result Formulas for null sectional curvatures of various space-time models.
Study finds conditions for certain warped product manifolds to be quasi-Einstein.
problem Conditions for quasi-Einstein sequential warped product manifolds.
method Investigated necessary and sufficient conditions for specific types of manifolds.
result Identified conditions for sequential warped product manifolds to be quasi-Einstein.
In this paper, we study Ricci-flat and Einstein Lorentzian multiply warped products. We also consider the case of having constant scalar curvatures for this class of warped products. Finally, after we introduce a new class of spacetimes called as generalized Kasner space-times, we apply our results to this kind of spac…
Study Ricci solitons on warped product manifolds and their implications.
problem Understanding Ricci solitons on warped product manifolds.
method Analyzes implications of Ricci solitons on base and fiber manifolds, and on warped product spaces with specific vector fields.
result Ricci solitons on warped product manifolds imply Ricci solitons on their factors.
Study investigates concircular curvature on warped products.
problem Effects of concircular flatness and symmetry on fibre and base manifolds.
method Investigated concircular flat and symmetric warped product manifolds, considered divergence free curvature tensor.
result Results applied to generalized Robertson-Walker and static space-times.
Study of conformal vector fields on specific manifolds and their applications.
problem Understanding conformal vector fields on doubly warped product manifolds.
method Complete study of two classes of conformal vector fields and Ricci solitons.
result Characterization of conformal vector fields and their properties.
The present article provides a study of 2−Killing vector fields on warped product manifolds as well as characterization of this structure on standard static and generalized Robertson-Walker space-times. Some conditions for a 2−Killing vector field on a warped product manifold to be parallel are obtained. Moreover, …
Warped product space-times generalize spherical symmetry results in relativity.
problem Generalizing spherical symmetry results to warped product space-times.
method Systematic geometric constructions, including the Kodama vector field and Hawking energy, with emphasis on signature independence.
result General Birkhoff-type theorems for warped product manifolds, applicable to non-Einstein solutions in general relativity.
In this paper, we study the Einstein warped products and multiply warped products with a quarter-symmetric connection. We also study warped products and multiply warped products with a quarter-symmetric connection with constant scalar curvature. Then apply our results to generalized Robertson-Walker spacetimes with a q…
The paper examines conditions for Einstein-like classes in doubly warped product manifolds.
problem Conditions for a factor manifold to be in the same Einstein-like class as the entire doubly warped product manifold.
method Analysis of the Ricci tensor and warping functions.
result Sufficient and necessary conditions for a factor manifold to inherit the Einstein-like class of the entire manifold.
Introduces sequential warped products for Einstein's equation solutions.
problem Finding new solutions to Einstein's equation.
method Introduced sequential warped products and studied their geometry.
result Characterized geodesics, Killing vector fields, and conformal vector fields.
Warped product construction for Finsler manifolds with curvature conditions.
problem Constructing new Finslerian manifolds with specific curvature properties.
method Extending the warped product concept to Finsler metrics, particularly (α,β)-metrics. result Demonstrated the feasibility of constructing new Finslerian manifolds with prescribed curvature conditions.
Essentially, some conditions for the Riemannian factor and the warping function of a standard static space-time are obtained in order to guarantee that no nontrivial warping function on the Riemannian factor can make the standard static space-time Einstein.
The paper studies φ-static perfect fluid space-times in Einstein's General Relativity.
problem Analyzing the geometry of φ-static perfect fluid space-times. method Reduction of Einstein's Field Equations to the factors of a static warped product, introducing φ-curvatures. result Sharp sufficient conditions for a compact φ-SPFST with boundary to be isometric to the standard hemisphere. We study "warped Berger" solutions $\big(\mc S^1\times\mc S^3,G(t)\big)$ of Ricci flow: generalized warped products with the metric induced on each fiber {s}×SU(2) a left-invariant Berger metric. We prove that this structure is preserved by the flow, that these solutions develop finite-time neckpinch …
The paper studies how certain surfaces evolve in space-time.
problem Preserving the space-like condition of non-compact hypersurfaces.
method Prescribed mean curvature flow in generalized Robertson-Walker spaces.
result The flow preserves space-like condition and exists for infinite time.
The paper classifies time-like surfaces in a static space-time.
problem Classifying time-like surfaces in a static space-time.
method Constructing a pseudo-orthonormal frame field and analyzing invariants.
result Complete classification theorem for class~A surfaces. Study Codazzi tensors in space-times, linking to Cotton gravity.
problem Understanding Codazzi tensors and their role in space-times.
method Analyzing geometric properties and proving conditions for Codazzi tensors.
result Codazzi tensors restrict space-times, influencing energy-momentum tensors in Cotton gravity.
In the framework of standard static space times, we state a family of sufficient or necessary conditions for a set of physically reasonable energy and convergence conditions in relativity and related theories. We concentrate our study on questions about the sub-harmonicity of the warping function, the scalar curvature …
The article surveys recent results on warped and CR-warped product submanifolds in Kaehler manifolds.
problem Characterizing submanifolds in Kaehler manifolds using warped and CR-warped products.
method Analyzing properties of warped and CR-warped products in the context of Kaehler manifolds.
result Presented several results on the geometry of warped and CR-warped product submanifolds.
The paper examines Einstein doubly warped product manifolds with a semi-symmetric metric connection.
problem Characterizing Einstein doubly warped product manifolds with a semi-symmetric metric connection.
method Deriving curvature formulas and proving necessary and sufficient conditions for a manifold to be a warped product.
result Obtained results for Einstein doubly warped product manifolds and Einstein-like doubly warped product manifolds.
Generalizes warped product submersion to conformal case.
problem Understanding angles preservation in submersions.
method Introduces conformal warped product submersion.
result Fundamental tensors derived for conformal submersion.
The paper explores geometric properties of Riemannian warped product maps and their curvature.
problem Investigating the geometric properties of Riemannian warped product maps.
method The approach involves establishing conditions for geodesics, deriving curvature tensors, and examining various types of maps.
result Derivation of integral formula for scalar curvature of conformal Riemannian warped product maps.
Study Killing vector fields on warped and multiply warped products with a semi-symmetric metric connection.
problem Characterize Killing vector fields on complex geometric structures.
method Define and analyze semi-symmetric metric Killing vector fields on warped and multiply warped products.
result Characterized properties of Killing vector fields on specific geometric structures.
Study of Einstein equations in warped spaces to determine cosmological constants.
problem Understanding the origin of the cosmological constant in higher dimensions.
method Classification and analysis of (m+n)D and (1+n)D warped spaces satisfying Einstein equations. result Warping function can determine both (m+n)D and 4D cosmological constants. Study on warped product Yamabe solitons with constant fiber curvature.
problem Characterizing nontrivial warped product Yamabe gradient solitons.
method Investigation of warped product manifolds, derivation of scalar curvature estimates.
result Nontrivial warped product Yamabe gradient solitons have constant scalar curvature in the fiber.
The paper explores warped-like product metrics with exceptional holonomy groups.
problem Exploring new metrics with exceptional holonomy groups.
method Presented a general ansatz of warped-like product metric and studied specific examples.
result Explicit examples of (3+3+2) and (3+3+1) warped-like product manifolds with Spin(7) and G2 holonomy, respectively. Proves a theorem for a specific type of warped product space.
problem Analyzing warped product spaces.
method Uses the warped function \( f(r) = \cosh\left(r\sqrt{\frac{\lambda}{n-2}}
ight) \) to prove the theorem.
result Proves an almost splitting theorem for the specified warped product space.
Warped product affects divergences in information geometry.
problem Warped product's impact on divergences in information geometry.
method Study of warped product on information geometry.
result Warped product does not preserve canonical divergences.
The paper extends affine connection results to singular warped and twisted products.
problem Generalizing affine connections to singular warped and twisted products.
method Study of singular multiply warped products and singular twisted products with semi-symmetric metric and non-metric connections, discussing Koszul forms and curvature.
result Theoretical results on curvature and Koszul forms for singular multiply warped and twisted products.
The paper proves rigidity for submanifolds in warped product manifolds.
problem Rigidity of submanifolds in warped product manifolds.
method Dihedral extremality and rigidity theorem for submanifolds with polyhedral boundary.
result Dihedral rigidity results for hyperbolic polyhedra in flat warped product spaces.
Paper defines and studies Clairaut warped product Riemannian maps.
problem Understanding the geometry of specific Riemannian maps.
method Identify geodesic conditions, derive conditions for Clairaut maps, and calculate curvature.
result Found conditions for a warped product Riemannian map to be Clairaut.
Study on warped product pointwise semi-slant submanifolds in Sasakian and cosymplectic manifolds.
problem Investigate the geometry of pointwise semi-slant submanifolds and their warped products.
method Using the notion of pointwise slant submanifolds, investigate the geometry of pointwise semi-slant submanifolds and their warped products in Sasakian and cosymplectic manifolds.
result Prove the existence of no proper pointwise semi-slant warped product submanifolds other than contact CR-warped products in Sasakian manifolds.
The paper studies a new type of submanifolds in product spaces.
problem Characterizing and understanding warped product pointwise bi-slant submanifolds.
method Introduced and studied warped product pointwise bi-slant submanifolds of locally product Riemannian manifolds.
result Characterization results and non-trivial examples of these submanifolds.
Study properties of bi-warped product submanifolds in specific geometric spaces.
problem Characterize geometric properties of bi-warped product submanifolds.
method Analyze squared norm of second fundamental form and warping functions.
result Relationship between squared norm and warping functions for proper slant submanifolds.
The paper explores conditions for constructing gradient Ricci solitons on warped product spaces.
problem Conditions for constructing gradient Ricci solitons on warped product spaces.
method Analyzes conditions for expanding or steady gradient Ricci solitons on warped product spaces.
result Necessary and sufficient conditions for constructing gradient Ricci solitons on warped product spaces.
Study shows how certain metrics can be split into warped products.
problem Understanding conditions under which metrics can be split as warped products.
method Investigating warped area-minimizing hypersurfaces and spectral Ricci/scalar curvature bounds.
result Metrics can be locally split as warped products under specific curvature conditions.
Characterizes and examines gradient solitons on doubly warped product manifolds.
problem Understanding gradient solitons on specific manifold structures.
method Characterizations and examinations of various types of gradient solitons on doubly warped product manifolds.
result Effects of gradient solitons on factor manifolds and specific curvature properties of doubly warped products.
The paper characterizes warped product submanifolds in LCS-manifolds.
problem Characterizing warped product submanifolds in LCS-manifolds.
method Analyzing contact CR-warped product and pseudo-slant submanifolds, and constructing examples.
result There do not exist any proper warped product bi-slant submanifolds of LCS-manifolds.
New findings on instability of Einstein metrics in warped products.
problem Investigating the stability of warped product Einstein metrics.
method Exploiting the relationship between warped product Einstein metrics, quasi-Einstein metrics, and Ricci solitons, introducing a new destabilising perturbation (the Ricci variation).
result Certain infinite families of warped product Einstein metrics are unstable in high dimensions.
The paper modifies a warped product space to find conditions for constant height functions.
problem Finding sufficient conditions for the height function to be constant in a modified warped product space.
method The paper modifies the warped product space by adding a warping function and discusses the sufficient condition for the height of immersed surfaces.
result The paper establishes a sufficient condition for the height function to be constant in the modified warped product space.
The paper studies affine connections on singular warped products and their curvature.
problem Analyzing affine connections on singular warped products.
method Introducing semi-symmetric metric and non-metric Koszul forms, and expressing their curvature in terms of factor manifolds.
result Generalized results for singular multiply warped products.
In this paper we study the space of solutions to an overdetermined linear system involving the Hessian of functions. We show that if the solution space has dimension greater than one, then the underlying manifold has a very rigid warped product structure. We obtain a uniqueness result for prescribing the Ricci curvatur…
In this paper we study fundamental geometric properties of doubly warped product immersion which is an extension of warped product immersion. Moreover, we study geometric inequality for doubly warped products isometrically immersed in arbitrary Riemannian manifolds.
Study of warped product pointwise bi-slant submanifolds in Kaehler manifolds.
problem Characterize warped product pointwise bi-slant submanifolds in Kaehler manifolds.
method Extends previous studies on warped product slant submanifolds.
result Extends several important results on warped product slant submanifolds.
In this paper we study the warped product submanifolds of a Lorentzian paracosymplectic manifold and obtain some nonexistence results. We show that a warped product semi-invariant submanifold in the form {M=MT×fM⊥} of Lorentzian paracosymplectic manifold such that the characteristic vector field is n…
Characterizes metallic structures on product manifolds and provides conditions for warped products to be metallic.
problem Understanding metallic structures on product manifolds and conditions for warped products to be metallic.
method Characterization through metallic maps and necessary/sufficient conditions for warped products.
result Characterizes metallic structures and provides conditions for warped products to be metallic.
In this paper, we generalize the geometry of the product pseudo-Riemannian manifold equipped with the product Poisson structure (\cite{Nas2}) to the geometry of a warped product of pseudo-Riemannian manifolds equipped with a warped Poisson structure. We construct three bivector fields on a product manifold and show tha…